In many circumstances, the average value of a function is desired for some purpose. Averages may often be determined directly using each possible value of the function. However, determining averages directly may sometimes be impossible. Moreover, there are times when directly determining an average is possible, but it is not reasonable or feasible to do so. For example, the mathematical computation required to determine a true average may be too great in terms of time and/or processing resources, especially when the number of values in the set is tremendous (e.g., when there are billions or trillions of values) and/or when the computation is complex. Additionally, it may be financially cost prohibitive to secure each and every value of a function, especially when investigation or research is required (e.g., when millions of people would need to be polled for information).
Accordingly, an approximate average of a function is substituted from time to time for the true average. An approximate average of a function is computed using fewer than all of the actual values in the total set of values of the function.